Superiority of a mechanistic codon substitution model even for protein sequences in Phylogenetic analysis

Miyazawa, Sanzo

doi:10.1186/1471-2148-13-257

BMC Ecology and Evolution

Table 4 Comparisons between various amino acid and codon substitution models for the reference phylogenetic tree of the cpProt-55

From: Superiority of a mechanistic codon substitution model even for protein sequences in Phylogenetic analysis

Substitution model^a	K^b	Δℓ^c	ΔAIC^c	ΔBIC^c	β ^de	w ₀ ^d	${〈 e^{w_{ab}} 〉}^{f}$	${\hat{m}}^{g}$	^h	${\hat{α}}^{i}$
Amino acid substitution models
cpREV64-dG4r	1	0.0	0.0	0.0						0.292
LG-F-dG4r	20	-9935.0	19908.0	20051.6						0.339
mtREV-F-dG4r	20	-7875.1	15788.1	15931.7						0.259
WAG-F-dG4r	20	-7649.6	15337.2	15480.7						0.348
FLU-F-dG4r	20	-5732.4	11502.7	11646.3						0.269
cpREV10-F-dG4r	20	-5649.9	11337.8	11481.3						0.349
JTT-F-dG4r	20	-4671.9	9381.8	9525.3						0.347
cpREV64-F-dG4r	20	-803.8	1645.6	1789.2						0.345
Mechanistic codon substitution models
Equal-Constraint-10-F-dG4r	30	332.4	-606.8	-387.7	(0.0)	-0.000	1.000	0.109	2.556	0.287
EI-11-F-dG4r	31	565.0	-1070.0	-843.3	0.101	0.101	0.782	0.119	2.686	0.285
KHG-ML200-11-F-dG4r	31	1150.9	-2241.8	-2015.1	0.386	0.139	0.491	0.102	2.249	0.287
WAG-ML91+-11-F-dG4r	31	1164.8	-2269.5	-2042.9	0.334	0.065	0.475	0.161	2.648	0.286
LG-ML91+-11-F-dG4r	31	1179.4	-2298.7	-2072.0	0.271	0.165	0.548	0.139	2.666	0.286
JTT-ML91+-11-F-dG4r	31	1426.3	-2792.6	-2565.9	0.430	0.132	0.421	0.187	2.234	0.287
JTT-ML91+-11-F-dG8r	31	1666.2	-3272.3	-3045.6	0.435	0.134	0.418	0.182	2.237	0.295
Equal-Constraint-10-F-dG4s	30	346.8	-635.6	-416.4	(0.0)	-0.233	0.793	0.113	2.549	0.286
EI-11-F-dG4s	31	962.6	-1865.2	-1638.5	0.264	-0.255	0.341	0.135	2.727	0.262
KHG-ML200-11-F-dG4s	31	1472.2	-2884.3	-2657.7	0.434	-0.672	0.199	0.101	2.326	0.284
WAG-ML91+-11-F-dG4s	31	1632.9	-3205.8	-2979.1	0.607	-0.344	0.189	0.167	2.633	0.258
LG-ML91+-11-F-dG4s	31	1742.9	-3425.8	-3199.1	0.544	0.005	0.248	0.148	2.630	0.276
JTT-ML91+-11-F-dG4s	31	1886.9	-3713.7	-3487.1	0.788	0.221	0.235	0.191	2.198	0.253
JTT-ML91+-11-F-dG8s	31	2176.2	-4292.4	-4065.7	0.854	0.257	0.218	0.200	2.170	0.275
Equal-Constraint-10-F-dG4sf	87	1224.3	-2276.5	-1626.7	(0.0)	-0.174	0.840	0.115	2.537	0.276
EI-11-F-dG4sf	88	1920.6	-3667.2	-3009.8	0.279	-0.231	0.335	0.135	2.665	0.251
KHG-ML200-11-F-dG4sf	88	2105.0	-4036.1	-3378.7	0.455	-0.626	0.200	0.102	2.296	0.286
WAG-ML91+-11-F-dG4sf	88	2320.8	-4467.5	-3810.1	0.633	0.060	0.270	0.165	2.528	0.249
LG-ML91+-11-F-dG4sf	88	2369.0	-4564.0	-3906.7	0.523	-0.007	0.256	0.147	2.557	0.269
JTT-ML91+-11-F-dG4sf	88	2542.1	-4910.2	-4252.8	0.787	0.308	0.255	0.188	2.168	0.249

^a"-F" means that the equilibrium frequencies are estimated to be equal to those in the alignment; equal codon usage is assumed. "-dGmr" and "-dGms" mean discrete gamma distributions with m categories of unequal probabilities for the rate variation and the variation of selective constraint across sites, respectively. "-dGmsf" means the equilibrium frequencies for respective categories are estimated from their posterior probabilities for sites. The number string in the model name indicates the number of parameters optimized for the substitution rate matrix, and the remaining strings denote a rate matrix or a selective constraint matrix used.
^bThe number of adjustable parameters.
^cDifference from the reference state;Δℓ = ℓ+ 217554.4, ΔAIC=AIC- 435110.9, and ΔBIC=BIC- 435118.5. The reference tree topology is the one reported in [35].
^d $w_{ab} = min [β w_{ab}^{estimate} + w_{0} (1 - δ_{ab}), 0]$ ; $w_{ab}^{estimate}$ is the one specified by the model name.
^eThe value parenthesized means that the parameter is fixed at the value specified.
^fThe average of $e^{w_{ab}}$ over all amino acid pairs {a,b}; $〈 e^{w_{ab}} 〉 \equiv \frac{1}{190} \sum_{a} \sum_{b > a} e^{w_{ab}}$ .
^gThe ratio of double to single and of triple to double nucleotide change exchangeability; $\hat{m} \equiv {\hat{m}}_{[tc] [ag]}$ .
^hThe ratio of mean transitional to mean transversional exchangeability; ${\hat{m}}_{tc | ag} / {\hat{m}}_{[tc] [ag]}$ .
ⁱThe shape parameter of a discrete gamma distribution for the variation of mutation rate or selective constraint across sites.

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